In known illumination devices for surgical microscopes having two or four observer channels (see European patent document EP-A1-661 020, German patent document DE-A1-43 31 635, and German patent document DE-A1-196 50 773), two deflection elements are used to reflect the illuminating ray bundle into the observer beam paths. They are arranged symmetrically with respect to the main observation beam paths, thereby resulting in an asymmetry in the assistant observer beam paths (see, e.g., FIG. 2 in German patent document DE-A1-43 31 635). The illumination devices described have, in practice, the following disadvantages in terms of the red reflection:                a) The main observer and the assistant observer, who actually should be seeing the same thing, receive different red reflections.        b) Since the illuminating mirrors are arranged on only one side, “rolling” of a patient's eye in its socket can modify the red reflection of both observers.        